A recent study by Allstate Insurance Co. finds that 82% of teenagers have used c
ID: 3386721 • Letter: A
Question
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving ( The Wall Street Journal , May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone. a. State the null and the alternative hypotheses to test the policy analyst’s objective. b. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? What is the p-value? c. At = 0.05 has the law been effective? d. Repeat this exercise using the critical value approach with = 0.05. A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving ( The Wall Street Journal , May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone. a. State the null and the alternative hypotheses to test the policy analyst’s objective. b. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? What is the p-value? c. At = 0.05 has the law been effective? d. Repeat this exercise using the critical value approach with = 0.05.Explanation / Answer
a)
Formulating the null and alternatuve hypotheses,
Ho: p >= 0.82
Ha: p < 0.82 [ANSWER]
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b)
As we see, the hypothesized po = 0.82
Getting the point estimate of p, p^,
p^ = x / n = 0.75
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.027166155
Getting the z statistic,
z = (p^ - po)/sp = -2.576735608 [ANSWER, TEST STATISTIC]
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c)
As this is a 1 tailed test, then, getting the p value,
p = 0.00498691
As P < 0.05, then we reject Ho. YES, THE LAW HAS BEEN EFFECTIVE.
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d)
At 0.05 left tailed test, we reject Ho if
z < -1.645.
Thus, as z < -1.645 here, then we reject Ho.
There is significant evidence that the proportion of those who use cellphone while driving has decreased. [CONCLUSION]